Axial Impact Buckling of a Column With Random Initial Imperfections

Abstract

Axial impact buckling of perfectly elastic bars with initial imperfections is considered in a probabilistic setting. It is assumed that the initial imperfection function involved a single parameter, which in turn is a continuous random variable with given probability distribution function. The structure is said to buckle if the absolute value of the total displacement exceeds a prescribed value. The probabilistic nature of the random, critical time when such a failure occurs for the first time, is studied.

Ellipsoidal-bound convex model for the non-linear buckling of a column with uncertain initial imperfection

“…In stochastic model, extensive knowledge of the probabilistic characteristics of the initial imperfection is required. Elishakoff [1] considered the axial impact buckling of perfectly elastic bars with initial imperfections in a probabilistic setting. Chryssanthopoulos and Poggi [2,3] represented the application of a probabilistic methodology to the design and analysis of stiffened and fiber-reinforced composite cylinders under axial compression.…”

Suddenly Applied Loads

“…In this case, it can be shown that the buckling wavelength scales with the inverse square root of the impact speed [50]. Extensive studies using similar approaches have focused on rapid application of axial loading on cylinders and shells [51][52][53]. Extensive studies using similar approaches have focused on rapid application of axial loading on cylinders and shells [51][52][53].…”

Uncertain initial imperfections via probabilistic and convex modeling: Axial impact buckling of a clamped beam

“…We represent the uncertainty in the initial imperfection profile so that we treat the coefficients A 0 and A 1 as random variables [5] with following truncated normal joint probability density function (pdf):…”

“…The study of the axial impact buckling of beams with simply supported boundary conditions and uncertain initial imperfections has been delt with by Lindberg [13], Elishakoff [5,6] and Ben-Haim and Elishakoff [2] and other authors.…”

“…Elishakoff [5] provided a closed form solution for a beam whose initial imperfection is proportional to the fundamental mode shape. He used Hoff's [9] criterion of stability, which states that failure is presumed to occur if the instantaneous displacement exceeds a specified threshold.…”